variable assumption

I have an expression in term of an independent variable $q$. Now, I would like to assume that $q$ is an arbitrary $14$-th root of unity (i.e. $q^{14}=1$).

It is not allow to evaluate in any primitive root of unity, say $\eta$, since the coefficients of my expression are in the $7$-th cyclotomic field (i.e. the field is generated by $\xi=e^{2\pi i/7}$), so $\eta$ is in the field.

I also tried with "assume(q^14==1)", but it didn't work.

How can I do?

Added after Bruno's comment: Here is an example. I have the expression

exp=q^16*xi^5 + (q^325-12*q^235)*xi^2.

where q is an independent variable and xi is the 7th-root of unity with least argument. In other words, I have an expression in terms of an independent variable q with coefficients in the 7-th cyclotomic field

K.<xi> = CyclotomicField(7)

Now, I want to assume that $q^{14}=1$, thus the resultant expression should be

Comments

You should describe a bit more what you've done, and what you are trying to do. For instance, you may include some (minimal) code that does not work as you wish. Why do you want to assume that $q$ is a 14-th root of unity? To find the solutions of some equation?

1 answer

Instead of thinking exp as a symbolic expression with the symbol q on which you pus assumptions, you should define it as a polynomial on the field F with indeterminate q, and then work modulo q^14-1. So, you can do: